JEE Main 2025 Jan 22 Shift 2, Physics Q23: Charge & discharge of a condenser

JEE Main2025Jan 22, Shift 2Physics

A parallel plate capacitor of area $A = 16 cm^{2}$ and separation between the plates 10 cm, is charged by a DC current. Consider a hypothetical plane surface of area $A_{0} = 3.2 cm^{2}$ inside the capacitor and parallel to the plates. At an instant, the current through the circuit is 6A. At the same instant the displacement current through $A_{0}$ is ________ mA.

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Solution

The displacement current density inside the capacitor is uniform across the plate area and equals the conduction current density in the external circuit:

$J_{d} = \frac{I _{conduction}}{A} = \frac{6}{16} A/cm^{2}$ .

The displacement current through the smaller hypothetical area $A_{0}$ is:

$I_{d}^{'} = J_{d} \times A_{0} = \frac{6}{16} \times 3.2 = 1.2 A = 1200 mA$ .

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JEE Main 2025 Jan 22 Shift 2, Physics Q23: Charge & discharge of a condenser

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